MathsCBSE Class 10 · Standard · Sample paper, session 2023-24 · 4 marks · Case-based

CBSE Class 10 Mathematics Standard sample paper 2023-24: question 36

From the official CBSE sample question paper for 2023-24, section E, question 36, for 4 marks. Try it first; the hints and our step-by-step solution are below.

Q36 · 4 marks · Case-basedCompetency-basedArithmetic Progressions

Manpreet Kaur is the national record holder for women in the shot-put discipline. Her throw of 18.86 m at the Asian Grand Prix in 2017 is the maximum distance for an Indian female athlete. Keeping her as a role model, Sanjitha is determined to earn gold in Olympics one day. Initially her throw reached 7.56 m only. Being an athlete in school, she regularly practiced both in the mornings and in the evenings and was able to improve the distance by 9 cm every week. During the special camp for 15 days, she started with 40 throws and every day kept increasing the number of throws by 12 to achieve this remarkable progress.

(i)
How many throws Sanjitha practiced on 11th day of the camp?
1 mark
(ii)
What would be Sanjitha's throw distance at the end of 6 weeks?
2 marks
OR
(ii)
When will she be able to achieve a throw of 11.16 m?
2 marks
(iii)
How many throws did she do during the entire camp of 15 days?
1 mark

Figure in the paper: Photograph of a female athlete in a red top and gloves, holding a shot-put at the side of her neck, in throwing position. See it in the official paper.

Source: official sample paper from cbseacademic.nic.in (PDF). See it in the full Sample paper 2023-24.

Hints

Open one hint at a time and try again before the next.

Hint 1

Both the daily throws and the weekly distances increase by a fixed amount, so each forms an AP.

Hint 2

Convert 9 cm to metres. The 7.56 m throw is where she starts, before any week of practice.

Hint 3

For the whole camp, use $S_{n} = \frac{n}{2} [2 a + (n - 1) d]$ with n = 15.

Step-by-step solution

Each step shows the marks it earns, as an examiner would award them. Checked by an independent re-solve from the question paper.

(i) Throws per day form an AP with $a = 40$ , $d = 12$ .
$a_{11} = a + 10 d = 40 + 10 \times 12 = 160$ throws
1 mark
(ii)(a) Distances form an AP with $a = 7.56$ m and $d = 9$ cm $= 0.09$ m. The initial throw is at the start, so the end of 6 weeks is the 7th term ( $n - 1 = 6$ ).
½ mark
(ii)(a) $a_{n} = a + (n - 1) d$
½ mark
(ii)(a) $a_{7} = 7.56 + 6 (0.09)$
½ mark
(ii)(a) $a_{7} = 7.56 + 0.54 = 8.1$ m
½ mark
(ii)(b) $a = 7.56$ m, $d = 0.09$ m, $a_{n} = 11.16$ m
½ mark
(ii)(b) $a_{n} = a + (n - 1) d \Rightarrow 11.16 = 7.56 + (n - 1) (0.09)$
½ mark
(ii)(b) $3.6 = (n - 1) (0.09)$
½ mark
(ii)(b) $n - 1 = \frac{3.6}{0.09} = 40 \Rightarrow n = 41$ .
So 11.16 m is the 41st term, which she reaches after 40 weeks of improvement (in the 41st term of the AP).
½ mark
(iii) $S_{n} = \frac{n}{2} [2 a + (n - 1) d]$
$S_{15} = \frac{15}{2} [2 (40) + 14 (12)]$
½ mark
(iii) $S_{15} = \frac{15}{2} [80 + 168] = \frac{15}{2} \times 248 = 1860$ throws
½ mark

Answer: (i) 160 throws; (ii)(a) 8.1 m; (ii)(b) 41st term, i.e. after 40 weeks (scheme: 41 weeks); (iii) 1860 throws

Where the marks are

(i) Uses $a_{11} = a + 10 d$ to get 160 (1 mark)
(ii)(a) Correct a and d in metres (½ mark)
(ii)(a) Writes the nth-term formula (½ mark)
(ii)(a) Substitutes $n - 1 = 6$ (½ mark)
(ii)(a) Gets 8.1 m (½ mark)
(ii)(b) Correct a, d and $a_{n}$ (½ mark)
(ii)(b) Forms the equation $11.16 = 7.56 + (n - 1) (0.09)$ (½ mark)
(ii)(b) Simplifies to $3.6 = (n - 1) (0.09)$ (½ mark)
(ii)(b) Gets n = 41 (½ mark)
(iii) Sum formula with substitution (½ mark)
(iii) Gets 1860 (½ mark)

Revise the chapter

Chapter: Arithmetic Progressions (notes, formulas, where marks are lost and every past question)
Topic: Finding nth Term from the Sum of n Terms

Practise this chapterBoard-style questions from Arithmetic Progressions, one at a time, marked against the answer key and marking points.Back to the full paperSample paper 2023-24 (Standard): every question, by section.

The question is transcribed from the official paper; figures are described in words. The solution, hints and chapter tag are ours. Spotted an error? Write tosupport@questionbuddy.in.

CBSE Class 10 Mathematics Standard sample paper 2023-24: question 36

Hints

Step-by-step solution

Revise the chapter

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